Question: The following line passes through point $(-5, 4)$ : $y = -\dfrac{2}{3} x + b$ What is the value of the $y$ -intercept $b$ ?
Answer: Substituting $(-5, 4)$ into the equation gives: $4 = -\dfrac{2}{3} \cdot -5 + b$ $4 = \dfrac{10}{3} + b$ $b = 4 - \dfrac{10}{3}$ $b = \dfrac{2}{3}$ Plugging in $\dfrac{2}{3}$ for $b$, we get $y = -\dfrac{2}{3} x + \dfrac{2}{3}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ $(-5, 4)$